Equations

Definition
An equation is a statement that expresses the equality of two mathematical expressions. An equation has an equal sign, a right side expression and a left side expression.

Examples of equations

3x + 3 = 2x + 4 : the left side of the equation is the expression 3x + 3 and the right side is 2x + 4.

2x + 3y = 2 - 2x : equation in two variables x and y.

Solutions of an Equation
If we substitute x by -3 in the equation 2x + 8 = -2x - 4, we obtain

left side: 2x + 8 = 2(-3) + 8 = -6 + 8 = 2

right side: -2x - 4 = -2(-3) - 4 = 6 - 4 = 2

Since a substitution of x = - 3 in the equation gives a true statement 2 = 2, we call -3 the solution or root of the given equation 2x + 8 = -2x - 4. The set of all solutions of an equation is called the solution set of the equation.